System Of Steady-state Equations Research Articles

RETRIAL QUEUEING SYSTEMS WITH FINITE NUMBER OF TRAFFIC SOURCES

Retrial (return call) queuing systems theory have rapidly developed since the 1980s. The classical queuing theory consider queues without call blocking; thus, given an idle channel, a call being in the system is forwarded to this channel immediately. Such models are obviously an idealized pattern of real processes. An important type of blocking systems is retrial (return call) systems. Retrial queues are various and widely used. However, virtually all systems studied are considered to have exponentially distributed time in the orbit, which often does not correspond to actual systems (air field, computer, telefone systems). In article closed queueing systems with deterministic retrial time and finite number of traffic sources on non-Markov type and were investigated. Embedded Markov chains and the system of steady-state equations were built. Systems solutions methods were derived. System functioning characteristics, such as efficiency of service channel, mean waiting time of request, mean number returns of request and so on, were determined.

Algorithmic computation of steady-state probabilities in an almost observable GI/M/c queue with or without vacations under state dependent balking and reneging

We consider an almost observable GI/M/c/N queue with customer impatience with or without multiple synchronous vacations under state-dependent balking. Upon arriving, a customer joins or refuses to join the system based on certain state dependent joining/balking probabilities. Once an arriving customer joins the system and finds all the servers busy, it initiates an exponentially distributed impatience timer with random duration T. An equilibrium balking strategy is discussed for constant balking as a special case of state-dependent balking. In the constant balking case, the waiting time of a customer in a queueing system has been associated with a linear cost-reward structure for estimating the net benefit if a customer chooses to participate in the system. A steady-state system of equations is obtained using the supplementary variable technique. After that, a recursive algorithm is proposed to obtain the stationary system-length distribution at pre-arrival and arbitrary epochs using those steady-state equations, from which the mean system sojourn time, the average reneging rate and the average balking rate are derived. Finally, we produce numerical results relating to system performance and its net benefit when investigated for different model parameters. The proposed model has applications in the modeling of balking and impatient behavior of incoming calls in a call center, multi-core computing, multi-path routing in delay sensitive communications networks.

Structure of plasmas generated by the interaction between metallic ions and neutral gas particles in a low-pressure arc

A numerical solution for the metallic-plasma-neutral-gas structure generated in a low-pressure arc is presented. The equations correspond to a spherically symmetric fluid-like steady model, valid for the outer region of the arc, and describe the ion slowing down by elastic scattering with the neutral particles. Technically, the obtention of the profiles of different magnitudes is complicated due to the existence of a critical point in the steady-state system of equations. The proposed approach to overcome this difficulty is to solve instead a pseudotransient system of equations which rapidly and efficiently relax to the stationary state. By employing this numerical method of second-order accuracy in space, the plasma and neutral gas density, the electron and ion drift velocities, the electron and neutral temperatures, and the electrostatic potential profiles are obtained from the border of the arc channel up to the discharge chamber wall. It is found that the value of the neutral gas filling pressure strongly influences the plasma density and plasma potential distributions. An important result is that metallic ions emitted from the arc channel deliver their kinetic energy to the filling gas in a gradual manner, up to a pressure-dependent point beyond which they move to the walls sustained against collisions with the gas by a self-consistent electric field. Near the mentioned point, the metallic ion density presents a peculiar behavior, showing an increase that is more pronounced at high pressures; a pattern also evident in the electrostatic potential.

Cosmic-ray heating of cooling flows - A critical analysis

It is shown that a combination of MHD wave-mediated cosmic ray heating and thermal conduction could balance cooling in intracluster media and substantially reduce the rate of inflow. The appropriate system of steady state equations is solved, including a new self-consistent formulation for the cosmic-ray diffusivity. Models which can produce substantial positive temperature gradients in static configurations are found when conduction is reduced by a factor of 10 or more. These models have too-flat thermal pressure profiles compared with observations. It is found that cosmic-ray heating is unlikely either to stabilize positive density perturbations against condensation or to contribute appreciably to the powering of the optical filaments.

On a linear steady-state system of equations in microcontinuum fluid mechanics

Galerkin representations and integral representations are obtained for the linearized system of coupled differential equations governing steady incompressible flow of a micropolar fluid. The special case of 2-dimensional Stokes flows is then examined and further representation formulae as well as asymptotic expressions, are generated for both the microrotation and velocity vectors. With the aid of these formulae, the Stokes Paradox for micropolar fluids is established.